Nonlinear Complementarity Problems for n-Player Strategic Chance-constrained Games

Shangyuan Zhang; Shangyuan Zhang; Makhlouf Hadji; Abdel Lisser; Yacine Mezali

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Paper

Nonlinear Complementarity Problems for n-Player Strategic Chance-constrained Games

Topics: Game Theory; Stochastic Optimization

In Proceedings of the 11th International Conference on Operations Research and Enterprise Systems ICORES - Volume 1, 94-104, 2022

Authors: Shangyuan Zhang ^{1

;

2} ; Makhlouf Hadji ² ; Abdel Lisser ¹ and Yacine Mezali ²

Affiliations: ¹ CentraleSupelec, L2S, Université Paris Saclay, 3 Rue Curie Joliot, 91190, Gif-sur-Yvette, France ; ² Institut de Recherche Technologique SystemX, 8 Avenue de la Vauve, 91120 Palaiseau, France

Keyword(s): Chance-constrained Optimization, Game Theory, Nonlinear Complementarity Problem, Normal/Cauchy Distribution.

Abstract: In this paper, we focus on n-player strategic chance-constrained games where the payoff of each player follows either Cauchy or normal distribution. We transform the Nash equilibrium problem into its equivalent nonlinear complementarity problem (NCP) through the Karush-Kuhn-Tucker (KKT) conditions. Then, we prove the existence of the Nash equilibrium by the mean of Brouwer’s fixed-point theorem. In order to show the efficiency of our approach, we perform numerical experiments on a set of randomly generated instances.

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Paper citation in several formats:

Zhang, S.; Hadji, M.; Lisser, A. and Mezali, Y. (2022). Nonlinear Complementarity Problems for n-Player Strategic Chance-constrained Games. In Proceedings of the 11th International Conference on Operations Research and Enterprise Systems - ICORES; ISBN 978-989-758-548-7; ISSN 2184-4372, SciTePress, pages 94-104. DOI: 10.5220/0011005600003117

@conference{icores22,
author={Shangyuan Zhang. and Makhlouf Hadji. and Abdel Lisser. and Yacine Mezali.},
title={Nonlinear Complementarity Problems for n-Player Strategic Chance-constrained Games},
booktitle={Proceedings of the 11th International Conference on Operations Research and Enterprise Systems - ICORES},
year={2022},
pages={94-104},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0011005600003117},
isbn={978-989-758-548-7},
issn={2184-4372},
}

TY - CONF

JO - Proceedings of the 11th International Conference on Operations Research and Enterprise Systems - ICORES
TI - Nonlinear Complementarity Problems for n-Player Strategic Chance-constrained Games
SN - 978-989-758-548-7
IS - 2184-4372
AU - Zhang, S.
AU - Hadji, M.
AU - Lisser, A.
AU - Mezali, Y.
PY - 2022
SP - 94
EP - 104
DO - 10.5220/0011005600003117
PB - SciTePress